Interquartile, Semi-Interquartile and Midquartile Ranges

In a set of data, the quartiles are the values that divide the data into four equal parts. The median of a set of data separates the set in half.

The median of the lower half of a set of data is the lower quartile (LQ) or Q1.

The median of the upper half of a set of data is the upper quartile (UQ) or Q3 .

The upper and lower quartiles can be used to find another measure of variation call the interquartile range.

The interquartile range is the range of the middle half of a set of data. It is the difference between the upper quartile and the lower quartile.

Interquartile range = Q3Q1

In the above example, the lower quartile is 52 and the upper quartile is 58.

The interquartile range is 58 – 52 or 6.

Data that is more than 1.5 times the value of the interquartile range beyond the quartiles are called outliers .

Semi-interquartile range is one-half the difference between the first and third quartiles. It is half the distance needed to cover half the scores.  The semi-interquartile range is affected very little by extreme scores.  This makes it a good measure of spread for skewed distributions. It is obtained by evaluating .

The midquartile range is the numerical value midway between the first and third quartile.  It is one-half the sum of the first and third quartiles.  It is obtained by evaluating .

(The median, midrange and midquartile are not always the same value, although they may be.)